We have a Panasonic digital cordless phone set KX-TCD440NZ, i.e. base unit + 2 extra handsets. After many years of faithful service our base unit has finally sucked a kumara. Rather than buy a whole new set, would anyone know if it is possible to connect a new (probably Panasonic) base unit to our old handsets?

If both are DECT GAP compliant, you should be able to pair/register the handsets to a new base.

See if you can try it out. Take one of your handsets into a store and see if they have a display model you can test it out with. Usually you would need to put the base into pairing mode (Normally by holding the page/finder button on the base for a few seconds), and then attempt to register the handset via it's on screen menu.

You would usually need to know the base PIN for this, but it's likley to be 0000,1234 or 9999

That's a DECT phone. If your previous devices were DECT also, there's a chance you can pair them with the base station. However sometimes manufacturers don't adhere entirely to the DECT standard, so compatibility can change between generations.